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This paper exploits Web search logs for query expansion (QE) by presenting a new QE method based on path-constrained random walks (PCRW), where the search logs are represented as a labeled, directed graph, and the probability of picking an expansion term for an input query is computed by a learned combination of constrained random walks on the graph. The method is shown to be generic in that it covers most of the popular QE models as special cases and flexible in that it provides a principled mathematical framework in which a wide variety of information useful for QE can be incorporated in a unified way. Evaluation is performed on the Web document ranking task using a real-world data set. Results show that the PCRW-based method is very effective for the expansion of rare queries, i.e., low-frequency queries that are unseen in search logs, and that it outperforms significantly other state-of-the-art QE meth-ods.